The long-distance hiking trails called Sentiers de Grande Randonnée criss-cross France, as well as other parts of Europe. The GR trails are clearly marked by red and white horizontal lines.
The GR trails are marked on all hiking maps, and are often shown on the French Michelin road maps as well (look for a dashed line and the designation GR4, GR52A, etc.). If you run across a trail in your wanderings, try hiking along it in either direction for an hour or so. You will often find fascinating places not seen by the stick-to-the-road tourists.
Two the main GR trails in the Alpes-Maritimes area are the GR5, which goes North out of Nice up through the Parc du Mercantour, and the GR51 - Balcony of the Côte d'Azur, going east-west along the hills above the Mediterranian.
The dificulty of the trails varies considerably, from family-strolling-simple to experienced-hiker-hard. The majority of GR trails are suitable for average hikers (whoever they may be). If you don't have a guide book for the GR trail you're hiking, you can get a pretty good idea of the difficulty by looking at the map. Trails in the higher part of the Alps or going over mountain passes will often be impassable in the Winter. I have very rarely come across a part of a GR trail where it was necessary to clambor over rocks.
Some GR Trails
GR6. The GR6 grande randonnée trail begins in Saint Foy-la-Grande (Gironde) on the Dordogne river 50 km east of Bordeaux, and crosses France for 1100 km to Fouillouse (Hautes-Alpes), near St Paul-sur-Ubaye in the Alpes-de-Haute-Provence.